Study of Henon's orbit transfer problem using the Lambert algorithm

Abstract

The problem of transfer orbits from one body back to the same body (the moon or a planet) is formulated as a Lambert problem and solved by Gooding's Lambert routines. Elliptic and circular orbits are considered for the moon or a planet and any type of orbit (elliptic, parabolic, or hyperbolic) is considered for the spacecraft. The solutions are plotted in terms of the true anomaly (instead of the eccentric anomaly) for several cases. The use of the true anomaly simplifies the solutions in several ways. The problem of transfers from this body to the corresponding £4 and LS points is also solved. Next, the same problem is studied in terms of the A V and the time required for the transfer. Among all of the possible transfer orbits, a small family with almost zero A V was studied in detail. A transfer from the moon to the corresponding Lagrangian equilibrium points £4 or LS is shown, as an example of a practical application of this theory.